If I'm playing Epic, and I use Jan Ors to roll 4 dice with my turbolaser attack, do I still add three hit results? Or would I only add two because of the cap?

The limit is to rolling. Adding a result is a dice modification, so it should not apply.

However: Jan Ors can only apply her ability to primary attacks, so she can't be used with a turbolaser anyway.

The maximums are for the number of dice rolled (Attack section of the Rules Reference on pages 4-5 ) and do not reference total results at all, so you would still get the 3 added results in the event you hit.

Edit: @Maui. Thanks, I forgot that limitation with her ability.

For future reference: